scholarly journals Numerical study of airfoil with wavy leading edge at high Reynolds number regime

2020 ◽  
Author(s):  
William Denner Pires Fonseca ◽  
Rafael Rosario Da Silva ◽  
Reinaldo Marcondes Orselli ◽  
Adson Agrico De Paula ◽  
Ricardo Galdino da Silva
Keyword(s):  
Reynolds Number ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Reynolds

In this work, a numerical study of flow around an airfoil with wavy leading edge is presented at a Reynolds number of 3X106. The flow is resolved by considering the RANS (Reynolds Average Navier-Stokes)equations. The baseline geometry is based on the NACA 0021 profile. The wavy leading edge has an amplitude of 3% and wavelength of 11%, both with respect to the airfoil chord. Cases without and with wavy leadingedges are simulated and compared. Initially, studies of the numerical sensitivity with respect to the obtained results, considering aspects such as turbulence modeling and mesh refinement, are carried out as well as bycomparison with corresponding results in the literature. Numerical data such as pressure distribution, shear stress lines on the wing surface, and aerodynamics coefficients are used to describe and investigate the flowfeatures around the wavy leading airfoil. Comparisons between the straight leading edge and the wavy leading edge cases shows an increase of the maximum lift coefficient as well as stall angle for the wavy leading edge configuration. In addition, at an angle of attack near the stall, the present numerical results shows an increase of the drag coefficient with the wavy leading edge airfoil when compared with the corresponding straight leading edge case.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

scholarly journals Effect of Leading-Edge Bulges on Aerodynamic Characteristics of Bionic Wingsail

2021 ◽  
Author(s):  
Chen Li ◽  
Peiting Sun ◽  
Hongming Wang
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Suction Surface ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Extension Direction ◽  
Lift And Drag

The leading-edge bulges along the extension direction are designed on the marine wingsail. The height and the spanwise wavelength of the protuberances are 0.1c and 0.25c, respectively. At Reynolds number Re=5×105, the Reynolds Averaged Navier-Stokes equations are applied to the simulation of the wingsail with the bulges thanks to ANSYS Fluent finite-volume solver based on the SST K-ω models. The grid independence analysis is carried out with the lift and drag coefficients of the wingsail at AOA = 8° and AOA=20°. The results show that while the efficiency of the wingsail is reduced by devising the leading-edge bulges before stall, the bulges help to improve the lift coefficient of the wingsail when stalling. At AOA=22° under the action of the leading-edge tubercles, a convective vortex is formed on the suction surface of the modified wingsail, which reduces the flow loss. So the bulges of the wingsail can delay the stall.

Turbulent Flow in Two-Inlet Channels

1993 ◽  
Vol 115 (4) ◽  
pp. 638-645 ◽  
Author(s):  
Hsiao C. Kao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
High Reynolds ◽  
Inflow Conditions ◽  
Number Form

The problem of turbulent flows in two-inlet channels has been studied numerically by solving the Reynolds-averaged Navier-Stokes equations with the k–ε model in a mapped domain. Both the high Reynolds number and the low Reynolds number form were used for this purpose. In general, the former predicts a weaker and smaller recirculation zone than the latter. Comparisons with experimental data, when applicable, were also made. The bulk of the present computations used, however, the high Reynolds number form to correlate different geometries and inflow conditions with the flow properties after turning.

scholarly journals Numerical Implementations for 2D Lid-Driven Cavity Flow in Stream Function Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
K. Poochinapan
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Operator Splitting ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Function Formulation ◽  
High Reynolds ◽  
Stream Function Formulation

The aim of this paper is to study the properties of approximations to nonlinear terms of the 2D incompressible Navier-Stokes equations in the stream function formulation (time-dependent biharmonic equation). The nonlinear convective terms are numerically solved by using the method with internal iterations, compared to the ones which are solved by using explicit and implicit schemes (operator splitting scheme Christov and Marinova; (2001)). Using schemes and algorithms, the steady 2D incompressible flow in a lid-driven cavity is solved up to Reynolds number Re =5000 with second-order spatial accuracy. The schemes are thoroughly validated on grids with different resolutions. The result of numerical experiments shows that the finite difference scheme with internal iterations on nonlinearity is more efficient for the high Reynolds number.

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